Question: Simplify the following expression: $z = \dfrac{6k^2 - 102k + 420}{k - 7} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $6$ , so we can rewrite the expression: $ z =\dfrac{6(k^2 - 17k + 70)}{k - 7} $ Then we factor the remaining polynomial: $k^2 {-17}k + {70} $ ${-7} {-10} = {-17}$ ${-7} \times {-10} = {70}$ $ (k {-7}) (k {-10}) $ This gives us a factored expression: $\dfrac{6(k {-7}) (k {-10})}{k - 7}$ We can divide the numerator and denominator by $(k + 7)$ on condition that $k \neq 7$ Therefore $z = 6(k - 10); k \neq 7$